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arXiv · 1609.01699

Poisson approximation of counts of subgraphs in random intersection graphs

Katarzyna Rybarczyk·Dudley Stark
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Abstract

Random intersection graphs are characterized by three parameters: $n$, $m$ and $p$, where $n$ is the number of vertices, $m$ is the number of objects, and $p$ is the probability that a given object is associated with a given vertex. Two vertices in a random intersection graph are adjacent if and only if they have an associated object in common. When $m=\lfloor n^\alpha\rfloor$ for constant $\alpha$, we provide a condition, called {\em strictly $\alpha$-balanced}, for the Poisson convergence of the number of induced copies of a fixed subgraph.

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Katarzyna Rybarczyk, Dudley Stark. 2016-09-06. Poisson approximation of counts of subgraphs in random intersection graphs. https://arxiv.org/abs/1609.01699

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